It is well-known to manufacture mechanical parts through the technique consisting in winding reinforcing wires round a spindle driven into rotation. However, the wires are wound in coils with the axis of rotation of the spindle as the axis. In some prior processes, for manufacturing parts having several winding axes, the spindle is necessarily brought into rotation ground the various axes. The support of the winding spindle is then mechanically complex. On the contrary, our invention notably allows reinforcing wire loops to be obtained without rotating the spindle round the axis of the loops.